Laws of Motion & Friction · JEE Main previous year questions

A light string passing over a smooth light fixed pulley connects two blocks of masses $m_1$ and $m_2$. If the acceleration of the system is $g/8$, then the ratio of masses is:

1. A.$\frac{8}{1}$
2. B.$\frac{9}{7}$
3. C.$\frac{5}{3}$
4. D.$\frac{4}{3}$

1. A.$2\sqrt{10}\text{ m/s}$
2. B.$10\text{ m/s}$
3. C.$\sqrt{10}\text{ m/s}$
4. D.$20\text{ m/s}$

1. A.$\frac{g}{2}$
2. B.$\frac{g}{4}$
3. C.$\mathrm{g}$
4. D.$\frac{g}{3}$

A spherical body of mass $100\text{ g}$ is dropped from a height of $10\text{ m}$ from the ground. After hitting the ground, the body rebounds to a height of $5\text{ m}$. The impulse of force imparted by the ground to the body is given by : (given, $g=9.8{\text{ m/s}}^2$)

1. A.$43.2{\text{ kg ms}}^{-1}$
2. B.$2.39{\text{ kg ms}}^{-1}$
3. C.$4.32{\text{ kg ms}}^{-1}$
4. D.$23.9{\text{ kg ms}}^{-1}$

A block of mass $100\text{ kg}$ slides over a distance of $10\text{ m}$ on a horizontal surface. If the co-efficient of friction between the surfaces is $0.4$, then the work done against friction (in $J$) is :

1. A.$3900$
2. B.$4500$
3. C.$4200$
4. D.$4000$

In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are $70{\text{ ms}}^{-1}$ and $65{\text{ ms}}^{-1}$ respectively. If the wing area is $2{\text{ m}}^2$, the lift of the wing is _______ $N$. (Given density of air $=1.2{\text{ kg m}}^{-3}$)

A stone of mass $900\text{ g}$ is tied to a string and moved in a vertical circle of radius $1\text{ m}$ making $10\text{ rpm}$. The tension in the string, when the stone is at the lowest point is (if ${\pi }^2=9.8$ and $g=9.8{\text{ m/s}}^2$) :

1. A.$17.8\text{ N}$
2. B.$97\text{ N}$
3. C.$9.8\text{ N}$
4. D.$8.82\text{ N}$

1. A.$5:1$
2. B.$3:2$
3. C.$1:5$
4. D.$2:5$

Two bodies of mass $4\text{ g}$ and $25\text{ g}$ are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is :

1. A.$3:5$
2. B.$5:4$
3. C.$2:5$
4. D.$4:5$

Given below are two statements : Statement (I) : The limiting force of static friction depends on the area of contact and independent of materials. Statement (II) : The limiting force of kinetic friction is independent of the area of contact and depends on materials. In the light of the above statements, choose the most appropriate answer from the options given below :

1. A.Statement I is incorrect but Statement II is correct
2. B.Both Statement I and Statement II are correct
3. C.Both Statement I and Statement II are incorrect
4. D.Statement I is correct but Statement II is incorrect

A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of their kinetic energies is $\frac{7}{x}$, where $x$ is _______.

A bullet of $10\text{ g}$ leaves the barrel of gun with a velocity of $600\text{ m/s}$. If the barrel of gun is $50\text{ cm}$ long and mass of gun is $3\text{ kg}$, then value of impulse supplied to the gun will be :

1. A.$12\text{ Ns}$
2. B.$3\text{ Ns}$
3. C.$6\text{ Ns}$
4. D.$36\text{ Ns}$

Two bodies are having kinetic energies in the ratio $16:9$. If they have same linear momentum, the ratio of their masses respectively is :

1. A.$3:4$
2. B.$4:3$
3. C.$9:16$
4. D.$16:9$

A vehicle of mass $200\text{ kg}$ is moving along a levelled curved road of radius $70\text{ m}$ with angular velocity of $0.2\text{ rad/s}$. The centripetal force acting on the vehicle is:

1. A.$560\text{ N}$
2. B.$14\text{ N}$
3. C.$2800\text{ N}$
4. D.$2240\text{ N}$

In an experiment with sonometer when a mass of $180\text{ g}$ is attached to the string, it vibrates with fundamental frequency of $30\text{ Hz}$. When a mass $\mathrm{m}$ is attached, the string vibrates with fundamental frequency of $50\text{ Hz}$. The value of $\mathrm{m}$ is ___________ g.

To maintain a speed of 80 km/h by a bus of mass 500 kg on a plane rough road for 4 km distance, the work done by the engine of the bus will be ____________ kJ. [The coefficient of friction between tyre of bus and road is 0.04.]

A block of mass $5\text{ kg}$ starting from rest is pulled up on a smooth inclined plane making an angle of $30^{\circ }$ with horizontal with an effective acceleration of $1{\text{ ms}}^{-2}$. The power delivered by the pulling force at $t=10\text{ s}$ from the start is _________ $\text{W}$. [use $g=10{\text{ ms}}^{-2}$] (calculate the nearest integer value)

If the maximum load carried by an elevator is 1400 kg ( 600 kg - Passengers + 800 kg - elevator), which is moving up with a uniform speed of $3{\text{ m s}}^{-1}$ and the frictional force acting on it is 2000 N, then the maximum power used by the motor is _________ kW ($g=10{\text{ m/s}}^2$)

At any instant the velocity of a particle of mass $500\text{ g}$ is $\left(2t\hat{i}+3t^2\hat{j}\right){\text{ms}}^{-1}$. If the force acting on the particle at $t=1\text{ s}$ is $(\hat{i}+x\hat{j})\text{N}$. Then the value of $x$ will be:

1. A.$2$
2. B.$4$
3. C.$6$
4. D.$3$

The momentum of a body is increased by $50\%$. The percentage increase in the kinetic energy of the body is ___________ $\%$.

A bullet of mass $0.1\mathrm{kg}$ moving horizontally with speed $400\mathrm{m}{\mathrm{s}}^{-1}$ hits a wooden block of mass $3.9\mathrm{kg}$ kept on a horizontal rough surface. The bullet gets embedded into the block and moves $20\mathrm{m}$ before coming to rest. The coefficient of friction between the block and the surface is ____. (Given $\mathrm{g}=10m/{\mathrm{s}}^2$ )

1. A.$0.65$
2. B.$0.25$
3. C.$0.50$
4. D.$0.90$

A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of the string producing a fundamental frequency of 180 Hz will be _________ cm.

A body of mass $5\mathrm{kg}$ is moving with a momentum of $10\mathrm{kg}\mathrm{m}{\mathrm{s}}^{-1}$. Now a force of $2\mathrm{N}$ acts on the body in the direction of its motion for $5\mathrm{s}$. The increase in the Kinetic energy of the body is ____ $\mathrm{J}$.